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The unpredictability of random numbers is fundamental to both digital security and applications that fairly distribute resources. However, existing random number generators have limitations-the generation processes cannot be fully traced, audited, and certified to be unpredictable. The algorithmic steps used in pseudorandom number generators are auditable, but they cannot guarantee that their outputs were a priori unpredictable given knowledge of the initial seed. Device-independent quantum random number generators can ensure that the source of randomness was unknown beforehand, but the steps used to extract the randomness are vulnerable to tampering. Here, for the first time, we demonstrate a fully traceable random number generation protocol based on device-independent techniques. Our protocol extracts randomness from unpredictable non-local quantum correlations, and uses distributed intertwined hash chains to cryptographically trace and verify the extraction process. This protocol is at the heart of a public traceable and certifiable quantum randomness beacon that we have launched. Over the first 40 days of operation, we completed the protocol 7434 out of 7454 attempts -- a success rate of 99.7%. Each time the protocol succeeded, the beacon emitted a pulse of 512 bits of traceable randomness. The bits are certified to be uniform with error times actual success probability bounded by $2^{-64}$. The generation of certifiable and traceable randomness represents one of the first public services that operates with an entanglement-derived advantage over comparable classical approaches., Comment: 40 pages, 4 main figures, 10 supplementary figures

Long-distance optical quantum channels are necessarily lossy, leading to errors in transmitted quantum information, entanglement degradation and, ultimately, poor protocol performance. Quantum states carrying information in the channel can be probabilistically amplified to compensate for loss, but are destroyed when amplification fails. Quantum correction of the channel itself is therefore required, but break-even performance -- where arbitrary states can be better transmitted through a corrected channel than an uncorrected one -- has so far remained out of reach. Here we perform distillation by heralded amplification to improve a noisy entanglement channel. We subsequently employ entanglement swapping to demonstrate that arbitrary quantum information transmission is unconditionally improved -- i.e. without relying on postselection or post-processing of data -- compared to the uncorrected channel. In this way, it represents realisation of a genuine quantum relay. Our channel correction for single-mode quantum states will find use in quantum repeater, communication and metrology applications., Comment: 11 pages, 6 figures, supplementary included

Single-photon detectors based on the superconducting transition-edge sensor (TES) are used in a number of visible to near-infrared (VNIR) applications, particularly for photon-number-resolving measurements in quantum information science. To be practical for large-scale photonic quantum computing or for future spectroscopic imaging applications in astronomy, the size of VNIR TES arrays must be increased from a few pixels to many thousands. Historically, TES arrays have been read out with multiplexed superconducting quantum interference devices (SQUIDs), but the microsecond-duration pulse signals of VNIR TESs are notoriously difficult to multiplex. In this manuscript, we introduce the kinetic inductance current sensor (KICS), a more readily scalable readout technology that exploits the nonlinear kinetic inductance in a superconducting resonator to make sensitive current measurements. KICS devices can replace SQUIDs for many applications because of their ability to measure fast, high slew-rate signals, their compatibility with standard microwave frequency-division multiplexing techniques, and their relatively simple fabrication. Here, we demonstrate the readout of a VNIR TES using a KICS with $3.7$ $\text{MHz}$ of bandwidth. We measure a readout noise of $1.4$ $\text{pA}/\sqrt{\text{Hz}}$, considerably below the TES noise at frequencies of interest, and a TES energy resolution of $(0.137 \pm 0.001)$ $\text{eV}$ at $0.8$ $\text{eV}$, comparable to resolutions observed with non-multiplexed SQUID readouts., Comment: 14 pages, 8 figures

Genuine quantum-mechanical effects are readily observable in modern optomechanical systems comprising bosonic ("classical") optical resonators. Here we describe unique features and advantages of optical two-level systems, or qubits, for optomechanics. The qubit state can be coherently controlled using both phonons and resonant or detuned photons. We experimentally demonstrate this using charge-controlled InAs quantum dots (QDs) in surface-acoustic-wave resonators. Time-correlated single-photon counting measurements reveal the control of QD population dynamics using engineered optical pulses and mechanical motion. As a first example, at moderate acoustic drive strengths, we demonstrate the potential of this technique to maximize fidelity in quantum microwave-to-optical transduction. Specifically, we tailor the scheme so that mechanically assisted photon scattering is enhanced over the direct detuned photon scattering from the QD. Spectral analysis reveals distinct scattering channels related to Rayleigh scattering and luminescence in our pulsed excitation measurements which lead to time-dependent scattering spectra. Quantum-mechanical calculations show good agreement with our experimental results, together providing a comprehensive description of excitation, scattering and emission in a coupled QD-phonon optomechanical system., Comment: 19 pages, 4 main figures, 7 supplementary figures

Superconducting detectors are a promising technology for probing dark matter at extremely low masses, where dark matter interactions are currently unconstrained. Realizing the potential of such detectors requires new readout technologies to achieve the lowest possible thresholds for deposited energy. Here we perform a prototype search for dark matter--electron interactions with kinetic inductance detectors (KIDs), a class of superconducting detector originally designed for infrared astronomy applications. We demonstrate that existing KIDs can achieve effective thresholds as low as 0.2 eV, and we use existing data to set new dark matter constraints. The relative maturity of the technology underlying KIDs means that this platform can be scaled significantly with existing tools, enabling powerful new searches in the coming years., Comment: 6+6 pages, 4+3 figures

Self-assembled InAs quantum dots (QDs) are promising optomechanical elements due to their excellent photonic properties and sensitivity to local strain fields. Microwave-frequency modulation of photons scattered from these efficient quantum emitters has been recently demonstrated using surface acoustic wave (SAW) cavities. However, for optimal performance, a gate structure is required to deterministically control the charge state and reduce charge noise of the QDs. Here, we integrate gated QDs and SAW cavities using molecular beam epitaxy and nanofabrication. We demonstrate that with careful design of the substrate layer structure, integration of the two systems can be accomplished while retaining the optimal performance of each subsystem. These results mark a critical step toward efficient and low-noise optomechanical systems for microwave-to-optical quantum transduction.

The co-location of memory and processing is a core principle of neuromorphic computing. A local memory device for synaptic weight storage has long been recognized as an enabling element for large-scale, high-performance neuromorphic hardware. In this work, we demonstrate programmable superconducting synapses with integrated memories for use in superconducting optoelectronic neural systems. Superconducting nanowire single-photon detectors and Josephson junctions are combined into programmable synaptic circuits that exhibit single-photon sensitivity, memory cells with more than 400 internal states, leaky integration of input spike events, and 0.4 fJ programming energies (including cooling power). These results are attractive for implementing a variety of supervised and unsupervised learning algorithms and lay the foundation for a new hardware platform optimized for large-scale spiking network accelerators., Comment: 16 pages, 11 figures

We demonstrate superconducting single-photon detectors that integrate signals locally at each pixel. This capability is realized by the monolithic integration of superconducting-nanowire single-photon detectors with Josephson electronics. The motivation is to realize superconducting sensor elements with integrating capabilities similar to their CMOS-sensor counterparts. The pixels can operate in several modes. First, we demonstrate that photons can be counted individually, with each detection event adding an identical amount of supercurrent to an integrating element. Second, we demonstrate an active gain control option, in which the signal added per detection event can be dynamically adjusted to account for variable light conditions. Additionally, the pixels can either retain signal indefinitely to record all counts incurred over an integration period, or the pixels can record a fading signal of detection events within a decay time constant. We describe additional semiconductor readout circuitry that will be used in future work to realize scalable, large-format sensor arrays of superconducting single photon detectors compatible with CMOS array readout architectures.

III-V semiconductor quantum dots (QDs) are near-ideal and versatile single-photon sources. Because of the capacity for monolithic integration with photonic structures as well as optoelectronic and optomechanical systems, they are proving useful in an increasingly broad application space. Here, we develop monolithic circular dielectric gratings on bulk substrates -- as opposed to suspended or wafer-bonded substrates -- for greatly improved photon collection from InAs quantum dots. The structures utilize a unique two-tiered distributed Bragg reflector (DBR) structure for vertical electric field confinement over a broad angular range. Opposing ``openings" in the cavities induce strongly polarized QD luminescence without harming collection efficiencies. We describe how measured enhancements depend critically on the choice of collection optics. This is important to consider when evaluating the performance of any photonic structure that concentrates farfield emission intensity. Our cavity designs are useful for integrating QDs with other quantum systems that require bulk substrates, such as surface acoustic wave phonons.

A large-format mid-infrared single-photon imager with very low dark count rates would enable a broad range of applications in fields like astronomy and chemistry. Superconducting nanowire single-photon detectors (SNSPDs) are a mature photon-counting technology as demonstrated by their figures of merit. However, scaling SNSPDs to large array sizes for mid-infrared applications requires sophisticated readout architectures in addition to superconducting materials development. In this work, an SNSPD array design that combines a thermally coupled row-column multiplexing architecture with a thermally coupled time-of-flight transmission line was developed for mid-infrared applications. The design requires only six cables and can be scaled to larger array sizes. The demonstration of a 64-pixel array shows promising results for wavelengths between $\mathrm{3.4\,\mu m}$ and $\mathrm{10\,\mu m}$, which will enable the use of this single-photon detector technology for a broad range of new applications., Comment: 7 pages, 3 figures, 1 page supplementary material. The following article has been submitted to Applied Physics Letters

The distribution and verification of quantum nonlocality across a network of users is essential for future quantum information science and technology applications. However, beyond simple point-to-point protocols, existing methods struggle with increasingly complex state preparation for a growing number of parties. Here, we show that, surprisingly, multiparty loophole-free quantum steering, where one party simultaneously steers arbitrarily many spatially separate parties, is achievable by constructing a quantum network from a set of qubits of which only one pair is entangled. Using these insights, we experimentally demonstrate this type of steering between three parties with the detection loophole closed. With its modest and fixed entanglement requirements, this work introduces a scalable approach to rigorously verify quantum nonlocality across multiple parties, thus providing a practical tool towards developing the future quantum internet.

For the last 50 years, superconducting detectors have offered exceptional sensitivity and speed for detecting faint electromagnetic signals in a wide range of applications. These detectors operate at very low temperatures and generate a minimum of excess noise, making them ideal for testing the non-local nature of reality, investigating dark matter, mapping the early universe, and performing quantum computation and communication. Despite their appealing properties, however, there are currently no large-scale superconducting cameras - even the largest demonstrations have never exceeded 20 thousand pixels. This is especially true for one of the most promising detector technologies, the superconducting nanowire single-photon detector (SNSPD). These detectors have been demonstrated with system detection efficiencies of 98.0%, sub-3-ps timing jitter, sensitivity from the ultraviolet (250nm) to the mid-infrared (10um), and dark count rates below 6.2e-6 counts per second (cps), but despite more than two decades of development they have never achieved an array size larger than a kilopixel. Here, we report on the implementation and characterization of a 400,000 pixel SNSPD camera, a factor of 400 improvement over the previous state-of-the-art. The array spanned an area 4x2.5 mm with a 5x5um resolution, reached unity quantum efficiency at wavelengths of 370 nm and 635 nm, counted at a rate of 1.1e5 cps, and had a dark count rate of 1e-4 cps per detector (corresponding to 0.13 cps over the whole array). The imaging area contains no ancillary circuitry and the architecture is scalable well beyond the current demonstration, paving the way for large-format superconducting cameras with 100% fill factors and near-unity detection efficiencies across a vast range of the electromagnetic spectrum.

Superconducting nanowire single photon detectors (SNSPDs) are the highest-performing technology for time-resolved single-photon counting from the UV to the near-infrared. The recent discovery of single-photon sensitivity in micrometer-scale superconducting wires is a promising pathway to explore for large active area devices with application to dark matter searches and fundamental physics experiments. We present 8-pixel $1 mm^2$ superconducting microwire single photon detectors (SMSPDs) with $1\,\mathrm{\mu m}$-wide wires fabricated from WSi and MoSi films of various stoichiometries using electron-beam and optical lithography. Devices made from all materials and fabrication techniques show saturated internal detection efficiency at 1064 nm in at least one pixel, and the best performing device made from silicon-rich WSi shows single-photon sensitivity in all 8 pixels and saturated internal detection efficiency in 6/8 pixels. This detector is the largest reported active-area SMSPD or SNSPD with near-IR sensitivity published to date, and the first report of an SMSPD array. By further optimizing the photolithography techniques presented in this work, a viable pathway exists to realize larger devices with $cm^2$-scale active area and beyond.

We present multiplexed gradient descent (MGD), a gradient descent framework designed to easily train analog or digital neural networks in hardware. MGD utilizes zero-order optimization techniques for online training of hardware neural networks. We demonstrate its ability to train neural networks on modern machine learning datasets, including CIFAR-10 and Fashion-MNIST, and compare its performance to backpropagation. Assuming realistic timescales and hardware parameters, our results indicate that these optimization techniques can train a network on emerging hardware platforms orders of magnitude faster than the wall-clock time of training via backpropagation on a standard GPU, even in the presence of imperfect weight updates or device-to-device variations in the hardware. We additionally describe how it can be applied to existing hardware as part of chip-in-the-loop training, or integrated directly at the hardware level. Crucially, the MGD framework is highly flexible, and its gradient descent process can be optimized to compensate for specific hardware limitations such as slow parameter-update speeds or limited input bandwidth.

State readout of trapped-ion qubits with trap-integrated detectors can address important challenges for scalable quantum computing, but the strong rf electric fields used for trapping can impact detector performance. Here, we report on NbTiN superconducting nanowire single-photon detectors (SNSPDs) employing grounded aluminum mirrors as electrical shielding that are integrated into linear surface-electrode rf ion traps. The shielded SNSPDs can be successfully operated at applied rf trapping potentials of up to $\mathrm{54\,V_{peak}}$ at $\mathrm{70\,MHz}$ and temperatures of up to $\mathrm{6\,K}$, with a maximum system detection efficiency of $\mathrm{68\,\%}$. This performance should be sufficient to enable parallel high-fidelity state readout of a wide range of trapped ion species in typical cryogenic apparatus., Comment: 6 pages, 4 figures. The following article has been submitted to Applied Physics Letters

Surface acoustic waves (SAWs) coupled to quantum dots (QDs), trapped atoms and ions, and point defects have been proposed as quantum transduction platforms, yet the requisite coupling rates and cavity lifetimes have not been experimentally established. Although the interaction mechanism varies, small acoustic cavities with large zero-point motion are required for high efficiencies. We experimentally establish the feasibility of this platform through electro- and opto-mechanical characterization of tightly focusing, single-mode Gaussian SAW cavities at $\sim$3.6 GHz on GaAs. We explore the performance limits of the platform by fabricating SAW cavities with mode volumes approaching 6$\lambda^3$ and linewidths $\leq$1 MHz. Employing strain-coupled single InAs QDs as optomechanical intermediaries, we measure single-phonon optomechanical coupling rates $g_0 \approx 2\pi \times 1.2$ MHz. Sideband scattering rates thus exceed intrinsic phonon loss, indicating the potential for quantum optical readout and transduction of cavity phonon states. To demonstrate the feasibility of this platform for low-noise ground-state quantum transduction, we develop a fiber-based confocal microscope in a dilution refrigerator and perform single-QD resonance fluorescence sideband spectroscopy at mK temperatures. These measurements show conversion between microwave phonons and optical photons with sub-natural linewidths., Comment: 15 pages, 10 figures

Superconducting optoelectronic hardware is being explored as a path towards artificial spiking neural networks with unprecedented scales of complexity and computational ability. Such hardware combines integrated-photonic components for few-photon, light-speed communication with superconducting circuits for fast, energy-efficient computation. Monolithic integration of superconducting and photonic devices is necessary for the scaling of this technology. In the present work, superconducting-nanowire single-photon detectors are monolithically integrated with Josephson junctions for the first time, enabling the realization of superconducting optoelectronic synapses. We present circuits that perform analog weighting and temporal leaky integration of single-photon presynaptic signals. Synaptic weighting is implemented in the electronic domain so that binary, single-photon communication can be maintained. Records of recent synaptic activity are locally stored as current in superconducting loops. Dendritic and neuronal nonlinearities are implemented with a second stage of Josephson circuitry. The hardware presents great design flexibility, with demonstrated synaptic time constants spanning four orders of magnitude (hundreds of nanoseconds to milliseconds). The synapses are responsive to presynaptic spike rates exceeding 10 MHz and consume approximately 33 aJ of dynamic power per synapse event before accounting for cooling. In addition to neuromorphic hardware, these circuits introduce new avenues towards realizing large-scale single-photon-detector arrays for diverse imaging, sensing, and quantum communication applications., Comment: 23 pages, 20 figures

Single-photon detection via absorption in current-biased nanoscale superconducting structures has become a preferred technology in quantum optics and related fields. Single-mode fiber packaged devices have seen new records set in detection efficiency, timing jitter, recovery times, and largest sustainable count rates. The popular approaches to decreasing polarization sensitivity have thus far been limited to introduction of geometrically symmetric nanowire meanders, such as spirals and fractals, in the active area. The constraints on bending radii, and by extension, fill factors, in such designs limits their maximum efficiency. The discovery of single-photon sensitivity in micrometer-scale superconducting wires enables novel meander patterns with no effective upper limit on fill factor. This work demonstrates simultaneous low-polarization sensitivity ($1.02\pm 0.008$) and high detection efficiency ($> 91.8\%$ with $67\%$ confidence at $2\times10^5$ counts per second) across a $40$ nm bandwidth centered at 1550 nm in 0.51 $\mu\text{m}$ wide microwire devices made of silicon-rich tungsten silicide, with a $0.91$ fill factor in the active area. These devices boasted efficiencies of $96.5-96.9\% \pm 0.5\%$ at $1\times10^5$ counts per second for 1550 nm light., Comment: 18 pages, 13 figures (including supplementary document) Added citations in replacement version

Fast, efficient, and low power modulation of light at microwave frequencies is crucial for chip-scale classical and quantum processing as well as for long-range networks of superconducting quantum processors. A successful approach to bridge the gap between microwave and optical photons has been to use intermediate platforms such as acoustic waves, which can couple efficiently to a variety of quantum systems. Here, we use gigahertz-frequency focusing surface acoustic wave cavities on GaAs that are piezo-electrically coupled to superconducting circuits and parametrically coupled, via strain, to photons scattered from InAs quantum dots . We demonstrate strong modulation of single photons with a half-wave voltage as low as 44 mV, and subnatural modulation sideband linewidths. These demonstrations pave the way for efficient and low-noise transduction of quantum information between microwave and optical domains.

We demonstrate the fabrication of micron-wide tungsten silicide superconducting nanowire single-photon detectors on a silicon substrate using laser lithography. We show saturated internal detection efficiencies with wire widths from 0.59$\mu$m to 1.43$\mu$m under illumination at 1550nm. We demonstrate both straight wires, as well as meandered structures. Single-photon sensitivity is shown in devices up to 4mm in length. Laser-lithographically written devices allow for fast and easy structuring of large areas while maintaining a saturated internal efficiency for wire width around 1$\mu$m., Comment: 5 pages, 7 figures

Although superconducting nanowire single-photon detectors (SNSPDs) are a promising technology for quantum optics, metrology, and astronomy, they currently lack a readout architecture that is scalable to the megapixel regime and beyond. In this work, we have designed and demonstrated such an architecture for SNSPDs, called the thermally-coupled imager (TCI). The TCI uses a combination of time-of-flight delay lines and thermal coupling to create a scalable architecture that can scale to large array sizes, allows neighboring detectors to operate independently, and requires only four microwave readout lines to operate no matter the size of the array. We give an overview of how the architecture functions, and demonstrate a proof-of-concept $32\times32$ imaging array. The array was able to image a free-space focused spot at 373 nm, count at 9.6 Mcps, and resolve photon location with greater than 99.83\% distinguishability.

We introduce the Broadband Reflector Experiment for Axion Detection (BREAD) conceptual design and science program. This haloscope plans to search for bosonic dark matter across the [10$^{-3}$, 1] eV ([0.24, 240] THz) mass range. BREAD proposes a cylindrical metal barrel to convert dark matter into photons, which a novel parabolic reflector design focuses onto a photosensor. This unique geometry enables enclosure in standard cryostats and high-field solenoids, overcoming limitations of current dish antennas. A pilot 0.7 m$^{2}$ barrel experiment planned at Fermilab is projected to surpass existing dark photon coupling constraints by over a decade with one-day runtime. Axion sensitivity requires $<10^{-20}$ W/$\sqrt{\textrm{Hz}}$ sensor noise equivalent power with a 10 T solenoid and 10 m$^{2}$ barrel. We project BREAD sensitivity for various sensor technologies and discuss future prospects., Comment: 5 pages, 2 figures + references and appendices, v2 matches journal version

Superconducting nanowires, a mature technology originally developed for quantum sensing, can be used as a target and sensor with which to search for dark matter interactions with electrons. Here we report on a 180-hour measurement of a tungsten silicide superconducting nanowire device with a mass of 4.3 nanograms. We use this to place new constraints on dark matter--electron interactions, including the strongest terrestrial constraints to date on sub-MeV (sub-eV) dark matter that interacts with electrons via scattering (absorption) processes., Comment: 5 pages + appendices, 5 figures. Matched published version

Uncovering the nature of dark matter is one of the most important goals of particle physics. Light bosonic particles, such as the dark photon, are well-motivated candidates: they are generally long-lived, weakly-interacting, and naturally produced in the early universe. In this work, we report on LAMPOST (Light $A'$ Multilayer Periodic Optical SNSPD Target), a proof-of-concept experiment searching for dark photon dark matter in the eV mass range, via coherent absorption in a multi-layer dielectric haloscope. Using a superconducting nanowire single-photon detector (SNSPD), we achieve efficient photon detection with a dark count rate (DCR) of $\sim 6\times10^{-6}$ counts/s. We find no evidence for dark photon dark matter in the mass range of $\sim 0.7$-$0.8$ eV with kinetic mixing $\epsilon \gtrsim 10^{-12}$, improving existing limits in $\epsilon$ by up to a factor of two. With future improvements to SNSPDs, our architecture could probe significant new parameter space for dark photon and axion dark matter in the meV to 10 eV mass range.

Superconducting nanowire single-photon detectors (SNSPDs) are the highest performing photon-counting technology in the near-infrared (NIR). Due to delay-line effects, large area SNSPDs typically trade-off timing resolution and detection efficiency. Here, we introduce a detector design based on transmission line engineering and differential readout for device-level signal conditioning, enabling a high system detection efficiency and a low detector jitter, simultaneously. To make our differential detectors compatible with single-ended time taggers, we also engineer analog differential-to-single-ended readout electronics, with minimal impact on the system timing resolution. Our niobium nitride differential SNSPDs achieve $47.3\,\% \pm 2.4\,\%$ system detection efficiency and sub-$10\,\mathrm{ps}$ system jitter at $775\,\mathrm{nm}$, while at $1550\,\mathrm{nm}$ they achieve $71.1\,\% \pm 3.7\,\%$ system detection efficiency and $13.1\,\mathrm{ps} \pm 0.4\,\mathrm{ps}$ system jitter. These detectors also achieve sub-100 ps timing response at one one-hundredth maximum level, $30.7\,\mathrm{ps} \pm 0.4\,\mathrm{ps}$ at $775\,\mathrm{nm}$ and $47.6\,\mathrm{ps} \pm 0.4\,\mathrm{ps}$ at $1550\,\mathrm{nm}$, enabling time-correlated single-photon counting with high dynamic range response functions. Furthermore, thanks to the differential impedance-matched design, our detectors exhibit delay-line imaging capabilities and photon-number resolution. The properties and high-performance metrics achieved by our system make it a versatile photon-detection solution for many scientific applications.

Schr\"odinger held that a local quantum system has some objectively real quantum state and no other (hidden) properties. He therefore took the Einstein-Podolsky-Rosen (EPR) phenomenon, which he generalized and called `steering', to require nonlocal wavefunction collapse. Because this would entail faster-than-light (FTL) information transmission, he doubted that it would be seen experimentally. Here we report a demonstration of EPR steering with entangled photon pairs that puts--in Schr\"odinger's interpretation--a non-zero lower bound on the amount of FTL information transmission. We develop a family of $n$-setting loss-tolerant EPR-steering inequalities allowing for a size-$d$ classical message sent from Alice's laboratory to Bob's. For the case $n=3$ and $d=2$ (one bit) we observe a statistically significant violation. Our experiment closes the efficiency and locality loopholes, and we address the freedom-of-choice loophole by using quantum random number generators to independently choose Alice's and Bob's measurement basis settings. To close the efficiency and locality loopholes simultaneously, we introduce methods for quickly switching between three mutually unbiased measurement bases and for accurately characterizing the efficiency of detectors. From the space-time arrangement of our experiment, we can conclude that if the mechanism for the observed bipartite correlations is that Alice's measurement induces wave-function collapse of Bob's particle, then more than one bit of information must travel from Alice to Bob at more than three times the speed of light., Comment: 10 pages plus 9 pages of supplemental material. v2 includes changes to text explaining Eq. (2), in section V.1., and in first paragraph of section VI

The nature of the magnetic-field driven superconductor-to-insulator quantum-phase transition in two-dimensional systems at zero temperature has been under debate since the 1980s, and became even more controversial after the observation of a quantum-Griffiths singularity. Whether it is induced by quantum fluctuations of the superconducting phase and the localization of Cooper pairs, or is directly driven by depairing of these pairs, remains an open question. We herein experimentally demonstrate that in weakly-pinning systems and in the limit of infinitely wide films, a sequential superconductor-to-Bose insulator-to-Fermi insulator quantum-phase transition takes place. By limiting their size smaller than the effective penetration depth, however, the vortex interaction alters, and the superconducting state re-enters the Bose-insulating state. As a consequence, one observes a direct superconductor-to-Fermi insulator in the zero-temperature limit. In narrow films, the associated critical-exponent products diverge along the corresponding phase boundaries with increasing magnetic field, which is a hallmark of the quantum-Griffiths singularity., Comment: 6 main figures, 11 supplementary Figures, 2 supplementary Movies. This is a preprint of an article published in Communications Physics. The final authenticated open-access version with updated figures and text is available for free from May 14, 2021 at https://doi.org/10.1038/s42005-021-00602-7

We demonstrate the integration of amorphous tungsten silicide superconducting nanowire single-photon detectors on titanium in-diffused lithium niobate waveguides. We show proof-of-principle detection of evanescently-coupled photons of 1550nm wavelength using bidirectional waveguide coupling for two orthogonal polarization directions. We investigate the internal detection efficiency as well as detector absorption using coupling-independent characterization measurements. Furthermore, we describe strategies to improve the yield and efficiency of these devices., Comment: 7 pages, 6 figures

Superconducting transition-edge sensors (TES) are extremely sensitive microcalorimeters used as photon detectors with unparalleled energy resolution. They have found application from measuring astronomical spectra through to determining the quantum property of photon-number, $\hat{n} {=} \hat{a}^{\dag} \hat{a}$, for energies from 0.6-2.33eV. However, achieving optimal energy resolution requires considerable data acquisition -- on the order of 1GB/min -- followed by post-processing, which does not allow access to energy information in real time. Here we use a custom hardware processor to process TES pulses while new detections are still being registered, allowing photon-number to be measured in real time as well as reducing data requirements by orders-of-magnitude. We resolve photon number up to n=16 -- achieving up to parts-per-billion discrimination for low photon numbers on the fly -- providing transformational capacity for applications of TES detectors from astronomy through to quantum technology., Comment: 16 pages, 11 figures, improved comparison between detectors, added information on appendix

The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric down-conversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling and quantum networks., Comment: 9 pages, 6 figures, added more discussions

Violating a nonlocality inequality enables the most powerful remote quantum information tasks and fundamental tests of quantum physics. Loophole-free photonic verification of nonlocality has been achieved with polarization-entangled photon pairs, but not with states entangled in other degrees of freedom. Here we demonstrate completion of the quantum steering nonlocality task, with the detection loophole closed, when entanglement is distributed by transmitting a photon in an optical vector vortex state, formed by optical orbital angular momentum (OAM) and polarization. As well as opening up a high-efficiency encoding beyond polarization, the critically-important demonstration of vector vortex steering opens the door to new free-space and satellite-based secure quantum communication devices and device-independent protocols., Comment: 7 pages, 3 figures

We show several techniques for using integrated-photonic waveguide structures to simultaneously characterize multiple waveguide-integrated superconducting-nanowire detectors with a single fiber input. The first set of structures allows direct comparison of detector performance of waveguide-integrated detectors with various widths and lengths. The second type of demonstrated integrated-photonic structure allows us to achieve detection with a high dynamic range. This device allows a small number of detectors to count photons across many orders of magnitude in count rate. However, we find a stray light floor of -30 dB limits the dynamic range to three orders of magnitude. To assess the utility of the detectors for use in synapses in spiking neural systems, we measured the response with average incident photon numbers ranging from less than $10^{-3}$ to greater than $10$. The detector response is identical across this entire range, indicating that synaptic responses based on these detectors will be independent of the number of incident photons in a communication pulse. Such a binary response is ideal for communication in neural systems. We further demonstrate that the response has a linear dependence of output current pulse height on bias current with up to a factor of 1.7 tunability in pulse height. Throughout the work, we compare room-temperature measurements to cryogenic measurements. The agreement indicates room-temperature measurements can be used to determine important properties of the detectors.

We report on the fabrication and characterization of single-photon-sensitive WSi superconducting detectors with wire widths from 1 {\mu}m to 3 {\mu}m. The devices achieve saturated internal detection efficiency at 1.55 {\mu}m wavelength and exhibit maximum count rates in excess of 10^5 s^-1. We also investigate the material properties of the silicon-rich WSi films used for these devices. We find that many devices with active lengths of several hundred microns exhibit critical currents in excess of 50% of the depairing current. A meandered detector with 2.0 {\mu}m wire width is demonstrated over a surface area of 362x362 {\mu}m^2, showcasing the material and device quality achieved.

We demonstrate adiabatically tapered fibers terminating in sub-micron tips that are clad with a higher-index material for coupling to an on-chip waveguide. This cladding enables coupling to a high-index waveguide without losing light to the buried oxide. A technique to clad the tip of the tapered fiber with a higher-index polymer is introduced. Conventional tapered waveguides and forked tapered waveguide structures are investigated for coupling from the clad fiber to the on-chip waveguide. We find the forked waveguide facilitates alignment and packaging, while the conventional taper leads to higher bandwidth. The insertion loss from a fiber through a forked coupler to a sub-micron silicon nitride waveguide is 1.1 dB and the 3 dB-bandwidth is 90 nm. The coupling loss in the packaged device is 1.3 dB. With a fiber coupled to a conventional tapered waveguide, the loss is 1.4 dB with a 3 dB bandwidth extending beyond the range of the measurement apparatus, estimated to exceed 250 nm.

Nonlinear frequency conversion plays a crucial role in advancing the functionality of next-generation optical systems. Portable metrology references and quantum networks will demand highly efficient second-order nonlinear devices, and the intense nonlinear interactions of nanophotonic waveguides can be leveraged to meet these requirements. Here we demonstrate second harmonic generation (SHG) in GaAs-on-insulator waveguides with unprecedented efficiency of 40 W$^{-1}$ for a single-pass device. This result is achieved by minimizing the propagation loss and optimizing phase-matching. We investigate surface-state absorption and design the waveguide geometry for modal phase-matching with tolerance to fabrication variation. A 2.0 $\mu$m pump is converted to a 1.0 $\mu$m signal in a length of 2.9 mm with a wide signal bandwidth of 148 GHz. Tunable and efficient operation is demonstrated over a temperature range of 45 $^{\circ}$C with a slope of 0.24 nm/$^{\circ}$C. Wafer-bonding between GaAs and SiO$_2$ is optimized to minimize waveguide loss, and the devices are fabricated on 76 mm wafers with high uniformity. We expect this device to enable fully integrated self-referenced frequency combs and high-rate entangled photon pair generation., Comment: 7 pages, 7 figures

With the growing availability of experimental loophole-free Bell tests, it has become possible to implement a new class of device-independent random number generators whose output can be certified to be uniformly random without requiring a detailed model of the quantum devices used. However, all of these experiments require many input bits in order to certify a small number of output bits, and it is an outstanding challenge to develop a system that generates more randomness than is consumed. Here, we devise a device-independent spot-checking protocol that consumes only uniform bits without requiring any additional bits with a specific bias. Implemented with a photonic loophole-free Bell test, we can produce 24% more certified output bits (1,181,264,237) than consumed input bits (953,301,640). The experiment ran for 91.0 hours, creating randomness at an average rate of 3606 bits/s with a soundness error bounded by $5.7\times 10^{-7}$ in the presence of classical side information. Our system will allow for greater trust in public sources of randomness, such as randomness beacons, and may one day enable high-quality private sources of randomness as the device footprint shrinks., Comment: The version accepted by Nature Physics. 6 pages (main text) + 20 pages (supplementary information), 7 figures

Just as classical information technology rests on a foundation built of interconnected information-processing systems, quantum information technology (QIT) must do the same. A critical component of such systems is the interconnect, a device or process that allows transfer of information between disparate physical media, for example, semiconductor electronics, individual atoms, light pulses in optical fiber, or microwave fields. While interconnects have been well engineered for decades in the realm of classical information technology, quantum interconnects (QuICs) present special challenges, as they must allow the transfer of fragile quantum states between different physical parts or degrees of freedom of the system. The diversity of QIT platforms (superconducting, atomic, solid-state color center, optical, etc.) that will form a quantum internet poses additional challenges. As quantum systems scale to larger size, the quantum interconnect bottleneck is imminent, and is emerging as a grand challenge for QIT. For these reasons, it is the position of the community represented by participants of the NSF workshop on Quantum Interconnects that accelerating QuIC research is crucial for sustained development of a national quantum science and technology program. Given the diversity of QIT platforms, materials used, applications, and infrastructure required, a convergent research program including partnership between academia, industry and national laboratories is required. This document is a summary from a U.S. National Science Foundation supported workshop held on 31 October - 1 November 2019 in Alexandria, VA. Attendees were charged to identify the scientific and community needs, opportunities, and significant challenges for quantum interconnects over the next 2-5 years., Comment: This is an updated version V2, including expanded text and listing of all co-authors. To whom correspondence should be addressed: Marko Lon\v{c}ar: loncar@seas.harvard.edu; Michael G. Raymer: raymer@uoregon.edu

W centers are trigonal defects generated by self-ion implantation in silicon that exhibit photoluminescence at 1.218 $\mu$m. We have shown previously that they can be used in waveguide-integrated all-silicon light-emitting diodes (LEDs). Here we optimize the implant energy, fluence and anneal conditions to maximize the photoluminescence intensity for W centers implanted in silicon-on-insulator, a substrate suitable for waveguide-integrated devices. After optimization, we observe near two orders of magnitude improvement in photoluminescence intensity relative to the conditions with the stopping range of the implanted ions at the center of the silicon device layer. The previously demonstrated waveguide-integrated LED used implant conditions with the stopping range at the center of this layer. We further show that such light sources can be manufactured at the 300-mm scale by demonstrating photoluminescence of similar intensity from 300 mm silicon-on-insulator wafers. The luminescence uniformity across the entire wafer is within the measurement error.

We propose and experimentally demonstrate a quantum state tomography protocol that generalizes the Wallentowitz-Vogel-Banaszek-W\'odkiewicz point-by-point Wigner function reconstruction. The full density operator of an arbitrary quantum state is efficiently reconstructed in the Fock basis, using semidefinite programming, after interference with a small set of calibrated coherent states. This new protocol is resource- and computationally efficient, is robust against noise, does not rely on approximate state displacements, and ensures the physicality of results., Comment: 19 pages, 10 Figures

We have investigated a series of superconducting bridges based on homogeneous amorphous WSi and MoSi films, with bridge widths w ranging from 2 um to 1000 um and film thicknesses d ~ 4-6 nm and 100 nm. Upon decreasing the bridge widths below the respective Pearl lengths, we observe in all cases distinct changes in the characteristics of the resistive transitions to superconductivity. For each of the films, the resistivity curves R(B,T) separate at a well-defined and field-dependent temperature T*(B) with decreasing the temperature, resulting in a dramatic suppression of the resistivity and a sharpening of the transitions with decreasing bridge width w. The associated excess conductivity in all the bridges scales as 1/w, which may suggest the presence of a highly conducting region that is dominating the electric transport in narrow bridges. We argue that this effect can only be observed in materials with sufficiently weak vortex pinning.

We present a 1024-element imaging array of superconducting nanowire single photon detectors (SNSPDs) using a 32x32 row-column multiplexing architecture. Large arrays are desirable for applications such as imaging, spectroscopy, or particle detection.

We demonstrate a polarization rotator integrated at the output of a GaAs waveguide producing type I second harmonic generation (SHG). Form-birefringent phase matching between the pump fundamental transverse electric (TE) mode near 2.0 $\mu$m wavelength and the signal fundamental transverse magnetic (TM) mode efficiently generates light at 1.0 $\mu$m wavelength. A SiN waveguide layer is integrated with the SHG device to form a multi-functional photonic integrated circuit. The polarization rotator couples light between the two layers and rotates the polarization from TM to TE or from TE to TM. With a TE-polarized 2.0 $\mu$m pump, type I SHG is demonstrated with the signal rotated to TE polarization. Passive transmission near 1.0 $\mu$m wavelength shows ~80 % polarization rotation across a broad bandwidth of ~100 nm. By rotating the signal polarization to match that of the pump, this SHG device demonstrates a critical component of an integrated self-referenced octave-spanning frequency comb. This device is expected to provide crucial functionality as part of a fully integrated optical frequency synthesizer with resolution of less than one part in 10$^{14}$., Comment: 7 pages, 7 figures

Nanophotonic waveguides with sub-wavelength mode confinement and engineered dispersion profiles are an excellent platform for application-tailored nonlinear optical interactions at low pulse energies. Here, we present fully air clad suspended-silicon waveguides for infrared frequency comb generation with optical bandwidth limited only by the silicon transparency. The achieved spectra are lithographically tailored to span 2.1 octaves in the mid-infrared (2.0-8.5 um or 1170--5000 cm-1) when pumped at 3.10 um with 100 pJ pulses. Novel fork-shaped couplers provide efficient input coupling with only 1.5 dB loss. The coherence, brightness, and the stability of the generated light are highlighted in a dual frequency comb setup in which individual comb-lines are resolved with 30 dB extinction ratio and 100 MHz spacing in the wavelength range of 4.8-8.5 um (2100-1170 cm-1). These sources are used for broadband gas- and liquid-phase dual-comb spectroscopy with 100 MHz comb-line resolution. We achieve a peak spectral signal-to-noise ratio of 10 Hz^0.5 across a simultaneous bandwidth containing 112,200 comb-lines. These results provide a pathway to further integration with the developing high repetition rate frequency comb lasers for compact sensors with applications in chip-based chemical analysis and spectroscopy.

We measure the detection efficiency of single-photon detectors at wavelengths near 851 nm and 1533.6 nm. We investigate the spatial uniformity of one free-space-coupled single-photon avalanche diode and present a comparison between fusion-spliced and connectorized fiber-coupled single-photon detectors. We find that our expanded relative uncertainty for a single measurement of the detection efficiency is as low as 0.70 % for fiber-coupled measurements at 1533.6 nm and as high as 1.78 % for our free-space characterization at 851.7 nm. The detection-efficiency determination includes corrections for afterpulsing, dark count, and count-rate effects of the single-photon detector with the detection efficiency interpolated to operation at a specified detected count rate.

The Wigner quasiprobability distribution of a narrowband single-photon state was reconstructed by quantum state tomography using photon-number-resolving measurements with transition-edge sensors (TES) at system efficiency 58(2)%. This method makes no assumptions on the nature of the measured state, save for the limitation on photon flux imposed by the TES. Negativity of the Wigner function was observed in the raw data without any inference or correction for decoherence., Comment: 10 pages, 7 figures

Entangling quantum systems with different characteristics through the exchange of photons is a prerequisite for building future quantum networks. Proving the presence of entanglement between quantum memories for light working at different wavelengths furthers this goal. Here, we report on a series of experiments with a thulium-doped crystal, serving as a quantum memory for 794 nm photons, an erbium-doped fibre, serving as a quantum memory for telecommunication-wavelength photons at 1535 nm, and a source of photon pairs created via spontaneous parametric down-conversion. Characterizing the photons after re-emission from the two memories, we find non-classical correlations with a cross-correlation coefficient of $g^{(2)}_{12} = 53\pm8$; entanglement preserving storage with input-output fidelity of $\mathcal{F}_{IO}\approx93\pm2\%$; and non-locality featuring a violation of the Clauser-Horne-Shimony-Holt Bell-inequality with $S= 2.6\pm0.2$. Our proof-of-principle experiment shows that entanglement persists while propagating through different solid-state quantum memories operating at different wavelengths., Comment: 3 figures in main-text and 5 figures in Supplemental Material

We demonstrate the tunable quantum beat of single photons through the co-development of core nonlinear nanophotonic technologies for frequency-domain manipulation of quantum states in a common physical platform. Spontaneous four-wave mixing in a nonlinear resonator is used to produce non-degenerate, quantum-correlated photon pairs. One photon from each pair is then frequency shifted, without degradation of photon statistics, using four-wave mixing Bragg scattering in a second nonlinear resonator. Fine tuning of the applied frequency shift enables tunable quantum interference of the two photons as they are impinged on a beamsplitter, with an oscillating signature that depends on their frequency difference. Our work showcases the potential of nonlinear nanophotonic devices as a valuable resource for photonic quantum information science.

The microscale integration of mid- and longwave-infrared photonics could enable the development of fieldable, robust chemical sensors, as well as highly efficient infrared frequency converters. However, such technology would be defined by the choice of material platform, which immediately determines the strength and types of optical nonlinearities available, the optical transparency window, modal confinement, and physical robustness. In this work, we demonstrate a new platform, suspended AlGaAs waveguides integrated on silicon, providing excellent performance in all of these metrics. We demonstrate low propagation losses within a span of nearly two octaves (1.26 to 4.6 $\mu$m) with exemplary performance of 0.45 dB/cm at $\lambda = 2.4$ $\mu$m. We exploit the high nonlinearity of this platform to demonstrate 1560 nm-pumped second-harmonic generation and octave-spanning supercontinuum reaching out to 2.3 $\mu$m with 3.4 pJ pump pulse energy. With mid-IR pumping, we generate supercontinuum spanning from 2.3 to 6.5 $\mu$m. Finally, we demonstrate the versatility of the platform with mid-infrared passive devices such as low-loss 10 $\mu$m-radius bends, compact power splitters with 96 $\pm$ 1% efficiency and edge couplers with 3.0 $\pm$ 0.1 dB loss. This platform has strong potential for multi-functional integrated photonic systems in the mid-IR.

The possibility for quantum and classical communication to coexist on the same fibre is important for deployment and widespread adoption of quantum key distribution (QKD) and, more generally, a future quantum internet. While coexistence has been demonstrated for different QKD implementations, a comprehensive investigation for measurement-device independent (MDI) QKD -- a recently proposed QKD protocol that cannot be broken by quantum hacking that targets vulnerabilities of single-photon detectors -- is still missing. Here we experimentally demonstrate that MDI-QKD can operate simultaneously with at least five 10 Gbps bidirectional classical communication channels operating at around 1550 nm wavelength and over 40 km of spooled fibre, and we project communication rates in excess of 10 THz when moving the quantum channel from the third to the second telecommunication window. The similarity of MDI-QKD with quantum repeaters suggests that classical and generalised quantum networks can co-exist on the same fibre infrastructure., Comment: 12 pages, 3 figures

Single self-assembled InAs/GaAs quantum dots are promising bright sources of indistinguishable photons for quantum information science. However, their distribution in emission wavelength, due to inhomogeneous broadening inherent to their growth, has limited the ability to create multiple identical sources. Quantum frequency conversion can overcome this issue, particularly if implemented using scalable chip-integrated technologies. Here, we report the first demonstration of quantum frequency conversion of a quantum dot single-photon source on a silicon nanophotonic chip. Single photons from a quantum dot in a micropillar cavity are shifted in wavelength with an on-chip conversion efficiency of approximately 12 %, limited by the linewidth of the quantum dot photons. The intensity autocorrelation function g(2)(tau) for the frequency-converted light is antibunched with g(2)(0) = 0.290 +/- 0.030, compared to the before-conversion value g(2)(0) = 0.080 +/- 0.003. We demonstrate the suitability of our frequency conversion interface as a resource for quantum dot sources by characterizing its effectiveness across a wide span of input wavelengths (840 nm to 980 nm), and its ability to achieve tunable wavelength shifts difficult to obtain by other approaches., Comment: Main text + supplementary information